Two-body continuum states in noninteger geometry

Wave functions, phase shifts, and corresponding elastic cross sections are investigated for two short-range interacting particles in a deformed external oscillator field. For this we use the equivalent d method employing a noninteger dimension d. Using a square-well potential, we derive analytic expressions for scattering lengths and phase shifts. In particular, we consider the dimension, d(E), for infinite scattering length, where the Efimov effect occurs by addition of a third particle. We give explicitly the equivalent continuum wave functions in d and ordinary three-dimensional space, and show that the phase shifts are the same in both methods. Consequently the d method can be used to obtain low-energy two-body elastic cross sections in an external field.

Automated summary

This study investigates wave functions, phase shifts, and corresponding elastic cross sections for two short-range interacting particles in a deformed external oscillator field. The equivalent d method with a noninteger dimension d is used. Analytic expressions for scattering lengths and phase shifts are derived using a square-well potential. The study also considers the dimension, d(E), for infinite scattering length and examines the occurrence of the Efimov effect by the addition of a third particle. It is shown that the phase shifts are the same in both d and three-dimensional space, indicating that the d method can be used to obtain low-energy two-body elastic cross sections in an external field.